Alternate Energy cost?

The mathematics of mpg

   A recent newspaper article reporting on what owners thought of their hybrid automobiles showed one exited driver jumping for joy. The Toyota Prius owner  was expressing her pleasure at the supposed 45 mpg and better she was getting from her new car. The article implied that owners of such cars would not be held captive to high gasoline prices. Technology would let them, in effect, tweak the nose of the oil companies. Good for them, I thought. But how long, I wondered, would it take to recoup the price difference from a less expensive car versus the Prius. The other car the Prius owner had been considering was a Toyota Echo. It has a combined rating (city and highway) of about 35 mpg and sell for, according to newspaper ads, $10,000 less than the Prius.
   To answer the question, I did a little figuring and came up with this equation: 

                           M = (D/C) / (1/m1-1/m2)

where M = miles driven to recoup a price difference, D = the cost difference of two candidate cars, C = cost of a gallon of gas, m1 = the mileage rating of less efficient car, and m2 = the mileage of the more efficient car. The difference should be a positive number.  
   So how long would it take to reclaim the cost difference for a more expensive hybrid automobile? At $1.40/gallon for gas and a $10,000 price difference: More than 1.12 million miles. That's a distance few people drive in the same car. Of course the equation does not account for maintenance, repair, and insurance. But if these incidentals push up the cost of the hybrid automobile, the mileage figure M also rises.
   The equation works best when the more expensive car has a higher mpg rating. It also allows comparisons of, say, a used mid-sized sedan that averages 25 mpg going for $7,000, and a small car rated at 35 mpg overall with a list of about $12,000. In this case, you'd have to drive the more expensive car over 313,000 mi. to reclaim the price difference.

   The equation also lets you ask, for kicks: What must the cost of gas be before the more expensive car makes sense within, say, 100,000 mi?  Solving for C and using values for the first two cars, the cost of gas would have to rise to more than $15/gal. Right now that seems unlikely. 
   A few conclusions one might reach from this simple exercise is that new cars are not a good deal when compared to used vehicles and when its important to save money on gas. Or you might conclude that a new car would rarely be less expensive to own than a reliable used car. And when the price of gas reaches $15/gal, even a car that gets 45 mpg will be considered a gas hog. At that point, you may as well take the bus, ride a bike, or put out your thumb.
   --Paul Dvorak, editorial director, Computer-Aided Engineering, contact him at pdvorak@penton.com.